Question

$D(2,1,0),E(2,0,0),F(0,1,0)$ are mid point of the sides $BC,CA,AB$ of $\Delta$ $ABC$ respectively, The the centroid of $\Delta$ABC is

• A. $\left(\frac{1}{3},\frac{1}{3},\frac{1}{3}\right)$
• B. $\left(\frac{4}{3},\frac{2}{3},0\right)$
• C. $(-\frac{1}{3},\frac{1}{3},\frac{1}{3})$
• D. $\left(\frac{2}{3},\frac{1}{3},\frac{1}{3}\right)$

Answer 1

The correct option is B $\left(\frac{4}{3},\frac{2}{3},0\right)$

Centroid of triangle coincide with the centroid of triangle formed by joing the mid-point of sides of triangle

So, centroid of $△ABC=$ centroid of $△DEF$

$=(\frac{2+2+0}{3},\frac{1+0+1}{3},\frac{0+0+0}{3})$

$=(\frac{4}{3},\frac{2}{3},0)$